Throughout history, circles have symbolized many things: unity, protection, the Sun, infinity, and the Olympic Games, to name a few. Of course, philosophers and symbologists aren’t the only people to have taken an interest in circles. Mathematicians have spent millennia studying them, too. Which is precisely why today’s article is all about circles. In particular, after a quick refresher of circle basics, we’re going to figure out why the equation for the circumference of a circle that we all learned in school works, and we’re also going to learn how this equation is used to set up lots of Olympic track and field events.

What Is a Circle?
My favorite way to define a circle is in terms of how to draw one. In the episode What Is Pi? we learned how to draw a circle arts-and-crafts style. To do this, start by cutting a 3-inch piece of string to serve as the radius of the circle. What’s the radius? It’s half the diameter. Okay, but what’s the diameter? As you’ll soon be able to test with your finished drawing, it’s the greatest distance between any two points on the circle. Now, pin one end of the string down with your finger near the center of a normal sheet of binder paper, and then hold the loose end of the string up against the lead of your pencil. Finally, pull the pencil so the string is taut and trace out your circle.

What does this all mean? Believe it or not, it means we’ve found a very good way to define a circle. Namely, a circle is the set of all points (that’s the curve you drew with your pencil) that are all the same distance from some common point (that’s the spot where you pinned the string down with your finger).